On Mining Webclick Streams for Path Traversal Patterns

On Mining Webclick Streams for Path Traversal Patterns

Hua-Fu Li

Department of Computer Science and Information Engineering National Chiao-Tung University No. 1001 Da-Shieh Rd., Hsinchu 300,

Taiwan, R.O.C.

[email protected]

Suh-Yin Lee

Department of Computer Science and Information Engineering National Chiao-Tung University No. 1001 Da-Shieh Rd., Hsinchu 300,

Taiwan, R.O.C.

[email protected]

Man-Kwan Shan

National Cheng-Chi University No. 64, Sec. 2, Zhi-Nan Rd., Wenshan,

Taipei 116, Taiwan, R.O.C.

[email protected]

ABSTRACT

Mining user access patterns from a continuous stream of Web-clicks presents new challenges over traditional Web usage mining in a large static Web-click database. Modeling user access patterns as maximal forward references, we present a single-pass algorithm StreamPath for online discovering frequent path traversal patterns from an extended prefix tree-based data structure which stores the compressed and essential information about user’s moving histories in the stream. Theoretical analysis and performance evaluation show that the space requirement of StreamPath is limited to a logarithmic boundary, and the execution time, compared with previous multiple-pass algorithms [2], is fast.

Categories and Subject Descriptors

H.2.8 [Database Management]: Databases Applications – data

mining.

General Terms

Algorithms, Performance.

Keywords

Web-click streams, data stream mining, path traversal patterns

1. INTRODUCTION

Recently, database and data mining communities have focus on a new data model, where data arrives in the form of continuous streams [1]. In the streaming data model, data does not take the form of persistent relations, but arrives sequentially (implicitly by arrival time or explicitly by timestamp), and is processed by an online algorithm whose workspace is insufficient to store all the data, so the main challenges of mining such streaming data (usually called stream data

mining) is constrained by limited resources of memory, processing time, and the total number of streaming data scan. Applications

include financial tickers, Web-log and click streams in Web applications, data feeds from sensor network, call detail records in telecommunications, online transactions in retail chains, etc. In this paper, we consider one of most important applications of data stream mining, namely, cost-efficient mining path traversal patterns over

Web-click stream.

The problem of mining path traversal patterns in a large static Web-click dataset was proposed by Chen et al. [2] for Web usage mining. In this paper, we extend the problem of path traversal pattern into a streaming problem. The problem can be modified as follows. Let S be a continuous stream of Web-clicks, where a Web-click Wc consists of an identifier UserID of the Web user and a Web-page reference r accessed by the user, i.e., Wc = (UserID, r). In such streaming environment, a segment of Web-click stream arrived at timestamp ti can be divided into a set of Web-click sequences. For example, a fragment of stream S = [(100, A)(100, B)(200, A)(300,

B)(200, B)(200, C)(300, C)(100, D)(200, A)(200, E)]ti, arrived at timestamp ti, can be classified into three Web-click sequences: {100, (A)(B)(D)}, {200, (A)(B)(C)(A)(E)}, and {300, (B)(C)}, where 100, 200, and 300 are the identifiers of Web users, and A, B, C, D, and E are references accessed by these users. For convenience, in the sequel, we drop the identifier of user, and denote a sequence of references

{(A)(B)(D)} as {ABD}. A Web-click sequence Wcs = <r1, r2, …, rk>

consists of a sequence of forward references and backward references accessed by a Web user. A backward reference means revisiting a previously visited page by the same user access. A maximal forward reference MFR is a forward reference path without any backward references. Hence, we can convert a Web-click sequence into several

maximal forward references, i.e., Wcs = MFR1, MFR2, …, MFRi,

where i ≥ 1. For instance, a Web-click sequence {ABCAE} consists of

two maximal forward references, namely, <ABC> and <AE>. Therefore, we can map the problem of finding frequent path traversal patterns into the one of finding frequent occurring consecutive sequences (called reference sequences) among all maximal forward references. The support of a reference sequence Rs, denoted by

Sup(Rs), is the number of maximal forward references containing Rs

divided by the total maximal forward references in S at timestamp ti. A reference sequence Rs is called a frequent traversal pattern if

Sup(Rs) ≥ MinSup, where MinSup is a minimum support threshold specified by the user. Consequently, the problem can be defined as follows. Given a minimum support threshold MinSup and a

continuous stream of Web-clicks S, the problem of mining Web-click streams for path traversal patterns is to discover the set of all frequent traversal patterns with respect to the characteristics of Web-click streams.

The objective of this paper is to mine the set of all frequent traversal patterns over a Web-click stream by one-scan the stream with limited memory usage and fast response time. Our algorithm

StreamPath has all of these characteristics, while none of previously

published methods can claim the same.

2. ONLINE ALGORITHM

2.1 Pattern-Growth Mining

The framework of StreamPath is derived from the well-known pattern-growth algorithm called FP-growth proposed by Han et al. [3] for mining static databases, which is a divide-and-conquer method, and it can be divided into three phases. First, FP-growth scans the database to find all frequent items, and constructs a Header-Table to record the summary information of these frequent items. Second, FP-growth makes the second database scan to construct a conditional frequent-pattern tree (FP-tree for short), which is an extended prefix-tree structure for compressing the size of the original database. Third, FP-growth uses a recursive search scheme to generate all frequent itemsets from the FP-tree. More details about the FP-growth method can be found in [3].

There are following problems in developing a pattern-growth based algorithm for mining Web-click streams:

1. It requires scanning the database twice, i.e., one for Header-Table construction, and another for FP-tree construction. Copyright is held by the author/owner(s).

WWW 2004, May 17–22, 2004, New York, New York, USA.

ACM 1-58113-912-8/04/0005.

B:1 C:2 E:2 F:1 O:1 G:1 A:2 A:2 B:1 C:1 E:1 F:1 O:1 G:1 B:1 C:1 E:1 F:1 O:1 C:2 E:2 F:1 O:1 E:2 F:1 O:1 F:1 O:1 O:1 G:1 Memory-Border C:1 E:1 G:1 G:1 B:1 C:3 E:3 F:1 O:1 G:2 D:1 A:2 A:2 B:1 C:1 E:1 F:1 O:1 G:1 B:1 C:1 E:1 F:1 O:1 C:3 E:2 F:1 O:1 E:3 F:1 O:1 F:1 O:1 O:1 G:2 Memory-Border C:1 E:1 G:1 G:2 D:1 E:1 G:1 D:1 E:1 G:1 E:2 G:1 C:2 A:1 A:2 C:1 E:1 G:1 C:3 E:2 E:3 G:2 Memory-Border C:1 E:1 G:1 G:2 E:1 G:1 C:2 E:2 G:1 A:1 A:2 G:3 C:3 E:3 E:3 G:2 Memory-Border C:2 E:2 G:1 G:2

2. The upper bound of the FP-tree’s memory usage is probably undetermined in such streaming environment.

These challenges show that static pattern-growth method can not appropriately meet the main performance requirements of mining Web-click streams. Hence, in this paper, we propose a modified pattern-growth framework, called stream-efficient pattern-growth, to satisfy the major performance requirements, namely, single-pass, bounded memory, and real-time, of data stream mining.

2.2 Stream-Efficient Pattern-Growth Mining

Algorithm StreamPath has two major features, namely online

dynamic maintaining StreamHT (Streaming Header-Table), and efficient constructing a StreamFP-tree (Streaming Frequent-Pattern tree) in a continuous stream of Web-clicks.

To illustrate these features of StreamPath, we will use the following example as a running example. Consider a fragment of example online Web-click stream S arrived at timestamp t; that is,

S=[(100, A)(100, B)(200, C)(300, C)(100, C)(200, D)(100, E)(100, F)(200, E)(300, D)(100, O)(200, D)(100, A)(100, C)(300, F)(100, E)(200, G)(100, G)]t_{. After a hashing function of each individual Web} user, and the transform function of maximal forward references, we can obtain three Web-click sequences, namely, {ABCEFOACEG}, {CDEG}, and {CDF}, and four maximal forward references, i.e., <ABCEFO>, <ACEG>, <CDEG>, and <CDF>, where each capital letter indicates a Web-page reference, and we assume that the StreamHT contains at most seven frequent items, which is constrained by 1/MinSup. More details about maintaining frequent items over a streaming data can be found in [4]. After processing the first two maximal forward references in this stream, a StreamFP-tree and the StreamHT were constructed, as shown in Figure 1 (a). In Figure 1 (b), the StreamHT was broken (since the number of frequent items is greater than the maximal size of StreamHT, i.e., 8 > 7), while

StreamPath reads in the third maximal forward reference {CDEG}.

The nodes bounded by the dotted boxes were removed from the StreamFP-tree and reconstructs the StreamFP-tree and the StreamHT, as shown in Figure 1 (c) and Figure 1 (d), respectively. At this time, if a user query wants to output the current set of frequent traversal patterns, then StreamPath traverses the StreamFP-tree, as shown in Figure 1 (d), in depth first search (DFS) manner and generates a temporal list which containing the set of current (maximal) frequent traversal pattern ACE and CEG. From this running example, we can see that StreamPath has all of these characteristics, namely, single-scan, limited memory and real-time, in a streaming environment.

3. MEMORY ANALYSIS AND EXPERIMENTS

Let the StreamHT contains k items at any time. Therefore, we know

there are at most C k 2k/ frequent reference sequences in the current

Web-click stream seen so far. If we construct a StreamFP-tree for all these frequent traversal patterns, the tree has height k/2. In the first

level, there are C /2 1

1+

k _{nodes, in the second level, there are C} /2 2

2+

k

nodes, in the i-th level, there are C k i

i2+

/ _{nodes, and in the last level,}

the k/2 level, there are C k 2k/ nodes. Thus, the total number of nodes

is C /2 1 1+ k _{+ C} /2 2 2+ k _{+ C} k i i2+ / _{+…+ C k 2}k_/ = _∑ = 2 / 1 k i C  k i i2+ / _□

The space requirement of StreamPath consists of two parts: the working space needed to create a StreamHT, and the storage space needed for the StreamFP-tree construction. In worst case, the working space for StreamHT requires k entries. For storage, there are at most

    ∑ ∑ = = + K j j i i j i

C

nodes of the StreamFP-tree. Thus, this gives a total space

bound of O(k+∑ ∑    = = + K j j i i j i

C

Dude to lack of space, we only summarize the comparisons of

StreamPath and the algorithms, FS and SS, proposed in [2], using

synthetic datasets same as [2]. On the synthetic datasets, StreamPath outperforms FS and SS. There are two main reasons why StreamPath does better than FS and SS. First, there is no candidate generation in

StreamPath. Second, StreamPath needs only one streaming data scan.

4. CONCLUSIONS

The problem of mining data streams is much more complicated than traditional data mining due to the characteristics of streaming data. In this paper we present an efficient algorithm for mining path traversal patterns over Web-click streams. Based on our knowledge, algorithm

StreamPath is a first efficient approach for Web-click stream mining

satisfying the key properties of one streaming data scan, limited memory usage, and fast processing time for each streaming Web click.

ACKNOWLEDGEMENTS

The authors thank the reviewers for their valuable comments and suggestions with significantly improve the quality of this paper. The work was supported by the National Science Council of R.O.C. under grant no. NSC92-2213-E009-123.

REFERENCES

[1] Babcock, B., Babu, S., Datar, M., Motwani, R., and Widom, J. Models and Issues in Data Stream Systems. In Proc. of the 2002 ACM

Symposium on Principles of Database Systems, 2002.

[2] Chen, M.-S., Park, J.-S., and Yu, P. S. Efficient Data Mining for Path Traversal Patterns, IEEE Transactions on Knowledge and Data

Engineering (TKDE), 10(2):209-221, 1998.

[3] Han, J., Pei, J., Yin, Y., and Mao, R. Mining Frequent Patterns without Candidate Generation: A Frequent-pattern Tree Approach. Data Mining

and Knowledge Discovery: An International Journal, 8(1):53-87, 2004.

[4] Karp, R., Shenker, S., and Papadimitriou, C. A Simple Algorithm for Finding Frequent Elements in Streams and Bags. ACM Transactions on

Database Systems (TODS), 28(1):51-55, 2003.

(a) (b) (c) (d) Figure 1. (a) StreamFP-tree after the first two maximal forward references, (b) StreamFP-tree reconstruction, (c) StreamFP-tree maintenance using

StreamHT pruning, (d) Current status of StreamFP-tree after the first three maximal forward references {ABCEFO}, {ACEG}, and {CDEG}.

StreamFP-tree StreamFP-tree

StreamFP-tree StreamFP-tree StreamHT StreamHT StreamHT StreamHT